Implementations of data structures and algorithms inspired by Steven S. Skiena's The Algorithm Design Manual, The Second Edition.

Algorithms currently implemented:

Graphs

• A generic network flow algorithm for calculating the maximum flow possible in a network.
• A bipartite matching algorithm which uses a network flow algorithm to find the largest possible matching in a graph.
• Breadth-First Search
• Dijkstra's Algorithm for finding the shortest path.
• Floyd's Algorithm for finding all shortest path pairs in a graph.
• hamiltonian_cycle: Determine whether a graph G = (V, E) contains a hamiltonian cycle.
• Kruskal's Algorithm for finding the minimum-spanning-tree.
• Prim's Algorithm for finding the minimum-spanning tree.

Backtracking

• Backtracking for subsets and permutations.

Dynamic Programming

• A brute-force recursive partition-optimization routine.
• Matrix-based edit distance.
• Matrix-based integer partition.

Reductions

• is_satisfiable: Whether a given set of clauses C over a set of variables V can be satisfied via some truth assignment of each variable v_i.
• set_cover: Whether a set cover for a set X can be constructed from k subsets chosen from a family of subsets F.
• Translations into 3SAT for any satisfiability instance.
• vertex_cover_to_set: Solve a vertex cover instance by converting it to a satisfiability instance.
• vertex_cover_to_set_cover: Prove that set cover is NP-complete with a reduction from vertex cover.